Question

The width of a confidence interval will be:

A) Wider when the sample standard deviation is small than when s is large

B) Narrower for 95% confidence than 99% confidence

C) Narrower for 95% confidence than 90% confidence

C) Wider for a sample size of 100 for a sample size of 50

Answer 1

Theory

In Point Estimation we estimated an unknown parameter θ with the help of a statistic (called the Estimator). In Interval Estimation we calculate an Interval (t₁ , t₂), known to be Confidence Interval, with hope of that this interval will cover the real value of the parameter θ with certain pre-assigned probability.

P[t₁ ≤ θ ≤ t₂] =1- α

Now the Confidence Interval of mean is given by:

(Considering Normality Assumption which is almost true according to CLT)

Size of the interval is:

• So, size of

So, Option (A) is correct.

• size of

When, it is 95% C.I i.e. α = 0.05, then

When, it is 99% C.I i.e. α = 0.05, then

Logically if we increase the probability of the parameter values to be included the Interval becomes wider.

So, Option (B) is correct and Option (C) is not correct.

• 

So, Option (D) is correct. (which is misprinted as C)